A Simple Unified Framework for High Dimensional Bandit Problems

Stochastic high dimensional bandit problems with low dimensional structure are useful in different applications such as online advertising and drug discovery. In this work, we propose a simple unified algorithm for such problems and present a general analysis framework for the regret upper bound of our algorithm. We show that under some mild unified assumptions, our algorithm can be applied to different high dimensional bandit problems. Our framework utilizes the low dimensional structure to guide the parameter estimation in the problem, therefore our algorithm achieves the best regret bounds in the LASSO bandit, better bounds in the low-rank matrix bandit and the group sparse matrix bandit, as well as a novel bound in the multi-agent LASSO bandit.